Question

If the equations $4x+7y=10$ and $10x+ky=25$ represent coincident lines, then find the value of $k$ ?

• A. $\frac{35}{2}$
• B. $\frac{25}{2}$
• C. $\frac{35}{4}$
• D. $\frac{33}{2}$

Answer 1

The correct option is A $\frac{35}{2}$

The given equations are

$4x+7y=10\Rightarrow 4x+7y-10=0$

$10x+ky=25\Rightarrow 10x+ky-25=0$

Given that the lines are coincident.

$\therefore \frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

Here $a_1=4,a_2=10,b_1=7,b_2=k,c_1=-10,c_2=-25$

$\therefore \frac{a_1}{a_2}=\frac{4}{10}=\frac{2}{5},\frac{b_1}{b_2}=\frac{7}{k},\frac{c_1}{c_2}=\frac{-10}{-25}=\frac{2}{5}$

$\therefore \frac{7}{k}=\frac{2}{5}$

$\Rightarrow k=\frac{35}{2}$